A332839 Irregular triangle whose n-th row lists the integers x such that the number of nonprimes (i.e., 1 and composites) in the reduced residue set (RSS(x)) of x equals n, or 0 if there are no such x.

1, 2, 3, 4, 6, 8, 12, 18, 24, 30, 5, 10, 14, 20, 42, 60, 7, 9, 16, 36, 48, 90, 15, 22, 54, 84, 26, 28, 66, 120, 11, 21, 32, 40, 72, 78, 210, 13, 34, 50, 38, 44, 70, 150, 102, 114, 126, 17, 27, 46, 56, 96, 108, 180, 19, 33, 52, 132, 25, 45, 80, 168, 0, 23, 39, 58, 62, 110, 138

Offset

1,2

Links

Table of n, a(n) for n=1..69.

Abhijit A J, A. Satyanarayana Reddy, Number of non-primes in the set of units modulo n, arXiv:1907.09908 [math.GM], 2019. See p. 3.

Example

Triangle begins:
1, 2, 3, 4, 6, 8, 12, 18, 24, 30;
5, 10, 14, 20, 42, 60;
7, 9, 16, 36, 48, 90;
15, 22, 54, 84;
26, 28, 66, 120;
11, 21, 32, 40, 72, 78, 210;
...

Mathematica

t = Select[ Table[{ EulerPhi[n] - PrimePi[n] + PrimeNu[n], n}, {n, 2000}], #[[1]] <= 100 &]; c = Complement[Range[100], First /@ t]; Last /@ (Sort@ Join[ Transpose[{c, 0 c}], t]) (* Giovanni Resta, Feb 26 2020 *)

Crossrefs

Cf. A048597 (1st row), A072022 (least x), A074915 (largest x), A076366 (row lengths).

Sequence in context: A074733 A001461 A048597 * A319054 A074964 A017822

Adjacent sequences: A332836 A332837 A332838 * A332840 A332841 A332842

Keyword

nonn,tabf

Author

Michel Marcus, Feb 26 2020

Status

approved